"iCloud account password - algorithm for reset fails: Hello, some promises, likely algorithmic, have been made relating to - iCloud.com - account resetting that do not happen. Genuis Bar won't accept an appointment to assist as a request to reset is already with Apple, again. Multiple messages similar to this screenshot have been received over the past weeks, one saying 'wait 6 days', the proof so far is no update response advice is received. Any advice please folks?"
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Troubleshooting a Locked Apple Account:
Why the Wait?: It's saying "wait 6 days" because you've fiddled with resetting it so much. So, I would say, contact Apple by phone, and screenshare with them what you are seeing. Use my User Tip: Screensharing MacOS FaceTime to Easily Converse Over-the-Phone with Apple Support - Apple Support
While on the Phone...
Make Up a Scenario:
When it comes to Apple Account issues, Apple typically blows off calls, and tells you to take it to an Apple Store. So, make up a scenario. like "I am having issues with receiving messages.", and then say, "Oh! By the way: My Apple Account is locked, how do I go about fixing this?"
After you are Back into your Account...
Create a Recovery Key for you to use, for future avoidance of this. Store it in a location that only YOU are aware of, and only YOU have access to: Set Up a Recovery Hey for your Apple Account - Apple Support